2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

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1 College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply Use the distributive property to remove the parentheses Simplify and write your answer as an expression without negative exponents. These are multiplied together Rewrite them using the multiplication symbol = 8 Now divide. The rules of exponents say to subtract exponents when you are dividing = 8 8 Write the answer without negative exponents 3. Multiply and write the product in simplest form: You should factor first Factor numerator and denominator

2 Multiply across the top and then across the bottom Look for common factors that will cancel out 4. Solve for X: Multiply by y to get rid of fraction OR cross multiply Need to have x by itself Add b to both sides 5. Find an equation for the line parallel to y = 3x + 1 that goes through the point (0, 5). The slope-intercept form of a linear equation is written y = mx + b. A line is parallel to another line if they never intersect, that is, if the two slopes are equal. Therefore, the slope m of the parallel line is equal to 3. So we have y = 3x + b. We must now find the y-intercept b. To do this, we substitute the known point (0, 5) into the equation y = 3x + b, and solve for b

3 Now substitute the b=5 back into the equation y =3x +b to find the equation of the parallel line Solve the following equation by factoring: Check your answer. You should factor first Factor the trinomial The exponent is a hint that there are 2 possible solutions and 4 0 Set both factors equal to zero and solve both Get the variable by itself The answer is and 4 You must check your answer by substituting both values of n back into the original equation Check:

4 7. Simplify and then if appropriate, write in radical notation: 3 8 Remember: when multiplying you add the exponents. In order to add fractions, you must have a common denominator. 3 8 Multiply the constants then the variables // Find a common denominator Add exponents This is the answer, but it is not simplified 24 Simplified now put in radical notation The power under the radical (3) cannot be bigger than the index (2) The square root of a squared number becomes that number Simplified number written in radical notation 8. Find the slope, the x-intercept, and the y-intercept of the graph 2x + 4y = 7 First put the general form of the equation into the slope-intercept form. NOTE: There is more than one way to do this problem. Only one way is presented here To put in slope-intercept form, you need to get y by itself Commutative property allows you to re-order Still trying to get y by itself Now you can find the slope and y-intercept

5 Slope = 1 2 Y-intercept = 7 4 To find the x- intercept, set y = 0 and solve for x The x-intercept is 7/2 9. Use the quadratic formula to solve: Leave your answer in simplified radical form. Quadratic formula Remember: 0 is standard form of a quadratic equation Therefore: a = 1; b = 2; c = (-1) This has 2 solutions and and These answers can be simplified

6 Solve the inequality 1 your answer in interval notation. 3 and graph the solution on a number line, then give Multiply by 2 to get rid of denominator Add 3 to each to get x by itself 5 9 This is the solution Graph on a number line [ ) Interval notation is [5, 9). 11. The height h in feet of a rocket t seconds after launch is given by the equation: a) When will the rocket reach a height of 320 feet? b) When will the rocket be back on the ground? a) Substitute height (h) into equation Move all terms to one side of equal sign Use commutative property to rearrange terms Factor out common factor Factor Set both factors equal to zero and solve

7 5 4 There are two solutions The rocket will reach a height of 320 feet after 4 seconds on its way up and again after 5 seconds on its way back down. Ground level is 0 feet, so substitute 0 in for h and solve as you did in part a Use commutative property to rearrange order Factor out common factor Set both factors equal to zero and solve Reject t = 0 because time does not stand still. The rocket will be back on the ground after 9 seconds. 12. Write an equivalent expression with as many factors as possible removed from under the radical: Remember: The square root of a squares number is that number. For example: 4 Therefore Commutative property allows us to rearrange the order 13. Rationalize the denominator. Leave your answer in radical notation. Multiply by the conjugate (a b) and (a + b) are conjugates

8 Answer left in radical notation 14. Multiply Use the foil method or distributive property How long is a guy wire that reaches from the top of a 12 foot pole to a point on the ground 5 ft from the bottom of the pole? Hint: Draw a picture. 12 foot? 5 foot When the pole meets the ground, a right angle is formed. Because this is a right triangle, the Pythagorean Theorem can be used to find the length of the guy wire c The guy wire is 13 feet long

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